LMFDB - Embedded newform 531.2.i.c.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			64.2
Character	$\chi$	$=$	531.64
Dual form			531.2.i.c.307.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.827908 - 0.278955i) q^{2} +(-0.984570 - 0.748451i) q^{4} +(-0.302390 + 0.758941i) q^{5} +(3.54386 - 1.63956i) q^{7} +(1.58690 + 2.34050i) q^{8} +O(q^{10})$	\(q+(-0.827908 - 0.278955i) q^{2} +(-0.984570 - 0.748451i) q^{4} +(-0.302390 + 0.758941i) q^{5} +(3.54386 - 1.63956i) q^{7} +(1.58690 + 2.34050i) q^{8} +(0.462061 - 0.543981i) q^{10} +(-0.673485 + 2.42568i) q^{11} +(-0.389461 + 0.734601i) q^{13} +(-3.39136 + 0.368832i) q^{14} +(0.000818890 + 0.00294937i) q^{16} +(-0.290699 - 0.134491i) q^{17} +(-1.91157 + 0.420768i) q^{19} +(0.865754 - 0.520907i) q^{20} +(1.23424 - 1.82036i) q^{22} +(0.931329 - 5.68086i) q^{23} +(3.14543 + 2.97951i) q^{25} +(0.527358 - 0.499540i) q^{26} +(-4.71631 - 1.03814i) q^{28} +(9.85394 - 3.32018i) q^{29} +(9.06141 + 1.99457i) q^{31} +(0.306328 - 5.64989i) q^{32} +(0.203155 + 0.192438i) q^{34} +(0.172706 + 3.18537i) q^{35} +(5.32796 - 7.85815i) q^{37} +(1.69998 + 0.184884i) q^{38} +(-2.25617 + 0.496620i) q^{40} +(-0.0298218 - 0.181905i) q^{41} +(1.03564 + 3.73006i) q^{43} +(2.47859 - 1.88418i) q^{44} +(-2.35576 + 4.44343i) q^{46} +(1.19658 + 3.00318i) q^{47} +(5.33907 - 6.28564i) q^{49} +(-1.77298 - 3.34419i) q^{50} +(0.933264 - 0.431774i) q^{52} +(-0.900748 - 1.06044i) q^{53} +(-1.63729 - 1.24464i) q^{55} +(9.46116 + 5.69259i) q^{56} -9.08434 q^{58} +(-7.22303 + 2.61302i) q^{59} +(-6.55238 - 2.20775i) q^{61} +(-6.94562 - 4.17904i) q^{62} +(-1.82741 + 4.58645i) q^{64} +(-0.439750 - 0.517714i) q^{65} +(5.53784 + 8.16770i) q^{67} +(0.185553 + 0.349990i) q^{68} +(0.745590 - 2.68537i) q^{70} +(-1.91968 - 4.81804i) q^{71} +(-10.7876 + 1.17323i) q^{73} +(-6.60313 + 5.01957i) q^{74} +(2.19700 + 1.01644i) q^{76} +(1.59031 + 9.70048i) q^{77} +(6.91340 - 4.15966i) q^{79} +(-0.00248603 - 0.000270372i) q^{80} +(-0.0260535 + 0.158920i) q^{82} +(-0.375926 - 6.93356i) q^{83} +(0.189975 - 0.179954i) q^{85} +(0.183098 - 3.37704i) q^{86} +(-6.74606 + 2.27301i) q^{88} +(4.70823 - 1.58639i) q^{89} +(-0.175769 + 3.24187i) q^{91} +(-5.16880 + 4.89615i) q^{92} +(-0.152904 - 2.82015i) q^{94} +(0.258701 - 1.57800i) q^{95} +(-8.26507 - 0.898880i) q^{97} +(-6.17367 + 3.71458i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{3}{29}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.827908	−	0.278955i	−0.585419	−	0.197251i	0.0109784	−	0.999940i	$-0.496505\pi$
$2$	−0.827908	−	0.278955i	−0.585419	−	0.197251i	−0.596398	+	0.802689i	$0.703402\pi$
$3$		0			0
$3$		0			0
$4$	−0.984570	−	0.748451i	−0.492285	−	0.374225i
$5$	−0.302390	+	0.758941i	−0.135233	+	0.339409i	−0.980961	−	0.194205i	$-0.937787\pi$
$5$	−0.302390	+	0.758941i	−0.135233	+	0.339409i	0.845728	+	0.533614i	$0.179167\pi$
$6$		0			0
$7$	3.54386	−	1.63956i	1.33945	−	0.619697i	0.386353	−	0.922351i	$-0.373735\pi$
$7$	3.54386	−	1.63956i	1.33945	−	0.619697i	0.953101	+	0.302654i	$0.0978726\pi$
$8$	1.58690	+	2.34050i	0.561054	+	0.827493i
$9$		0			0
$10$	0.462061	−	0.543981i	0.146117	−	0.172022i
$11$	−0.673485	+	2.42568i	−0.203063	+	0.731369i	0.789930	+	0.613197i	$0.210117\pi$
$11$	−0.673485	+	2.42568i	−0.203063	+	0.731369i	−0.992993	+	0.118171i	$0.962297\pi$
$12$		0			0
$13$	−0.389461	+	0.734601i	−0.108017	+	0.203742i	−0.931628	−	0.363414i	$-0.881611\pi$
$13$	−0.389461	+	0.734601i	−0.108017	+	0.203742i	0.823611	+	0.567155i	$0.191956\pi$
$14$	−3.39136	+	0.368832i	−0.906378	+	0.0985745i
$15$		0			0
$16$	0.000818890		0.00294937i	0.000204722		0.000737343i
$17$	−0.290699	−	0.134491i	−0.0705047	−	0.0326190i	0.384320	−	0.923200i	$-0.374436\pi$
$17$	−0.290699	−	0.134491i	−0.0705047	−	0.0326190i	−0.454825	+	0.890581i	$0.650298\pi$
$18$		0			0
$19$	−1.91157	+	0.420768i	−0.438544	+	0.0965308i	−0.428754	−	0.903421i	$-0.641047\pi$
$19$	−1.91157	+	0.420768i	−0.438544	+	0.0965308i	−0.00978987	+	0.999952i	$0.503116\pi$
$20$	0.865754	−	0.520907i	0.193588	−	0.116478i
$21$		0			0
$22$	1.23424	−	1.82036i	0.263140	−	0.388103i
$23$	0.931329	−	5.68086i	0.194196	−	1.18454i	−0.692233	−	0.721674i	$-0.743373\pi$
$23$	0.931329	−	5.68086i	0.194196	−	1.18454i	0.886428	−	0.462866i	$-0.153179\pi$
$24$		0			0
$25$	3.14543	+	2.97951i	0.629085	+	0.595901i
$26$	0.527358	−	0.499540i	0.103423	−	0.0979679i
$27$		0			0
$28$	−4.71631	−	1.03814i	−0.891299	−	0.196190i
$29$	9.85394	−	3.32018i	1.82983	−	0.616542i	0.831714	−	0.555204i	$-0.187360\pi$
$29$	9.85394	−	3.32018i	1.82983	−	0.616542i	0.998117	−	0.0613384i	$-0.0195369\pi$
$30$		0			0
$31$	9.06141	+	1.99457i	1.62748	+	0.358235i	0.932605	−	0.360899i	$-0.117530\pi$
$31$	9.06141	+	1.99457i	1.62748	+	0.358235i	0.694872	+	0.719134i	$0.255461\pi$
$32$	0.306328	−	5.64989i	0.0541517	−	0.998769i
$33$		0			0
$34$	0.203155	+	0.192438i	0.0348407	+	0.0330029i
$35$	0.172706	+	3.18537i	0.0291926	+	0.538426i
$36$		0			0
$37$	5.32796	−	7.85815i	0.875911	−	1.29187i	−0.0795734	−	0.996829i	$-0.525356\pi$
$37$	5.32796	−	7.85815i	0.875911	−	1.29187i	0.955484	−	0.295043i	$-0.0953339\pi$
$38$	1.69998	+	0.184884i	0.275773	+	0.0299921i
$39$		0			0
$40$	−2.25617	+	0.496620i	−0.356731	+	0.0785225i
$41$	−0.0298218	−	0.181905i	−0.00465738	−	0.0284088i	0.984396	−	0.175970i	$-0.0563061\pi$
$41$	−0.0298218	−	0.181905i	−0.00465738	−	0.0284088i	−0.989053	+	0.147561i	$0.952858\pi$
$42$		0			0
$43$	1.03564	+	3.73006i	0.157934	+	0.568828i	0.999585	+	0.0288058i	$0.00917043\pi$
$43$	1.03564	+	3.73006i	0.157934	+	0.568828i	−0.841651	+	0.540022i	$0.818416\pi$
$44$	2.47859	−	1.88418i	0.373662	−	0.284050i
$45$		0			0
$46$	−2.35576	+	4.44343i	−0.347337	+	0.655148i
$47$	1.19658	+	3.00318i	0.174539	+	0.438059i	0.990056	−	0.140674i	$-0.0449268\pi$
$47$	1.19658	+	3.00318i	0.174539	+	0.438059i	−0.815517	+	0.578733i	$0.803548\pi$
$48$		0			0
$49$	5.33907	−	6.28564i	0.762725	−	0.897949i
$50$	−1.77298	−	3.34419i	−0.250737	−	0.472940i
$51$		0			0
$52$	0.933264	−	0.431774i	0.129420	−	0.0598763i
$53$	−0.900748	−	1.06044i	−0.123727	−	0.145663i	0.696811	−	0.717255i	$-0.254602\pi$
$53$	−0.900748	−	1.06044i	−0.123727	−	0.145663i	−0.820538	+	0.571592i	$0.806326\pi$
$54$		0			0
$55$	−1.63729	−	1.24464i	−0.220772	−	0.167827i
$56$	9.46116	+	5.69259i	1.26430	+	0.760705i
$57$		0			0
$58$	−9.08434			−1.19283
$59$	−7.22303	+	2.61302i	−0.940358	+	0.340186i
$59$	−7.22303	+	2.61302i	−0.940358	+	0.340186i
$60$		0			0
$61$	−6.55238	−	2.20775i	−0.838946	−	0.282674i	−0.133156	−	0.991095i	$-0.542511\pi$
$61$	−6.55238	−	2.20775i	−0.838946	−	0.282674i	−0.705790	+	0.708421i	$0.749408\pi$
$62$	−6.94562	−	4.17904i	−0.882094	−	0.530739i
$63$		0			0
$64$	−1.82741	+	4.58645i	−0.228426	+	0.573307i
$65$	−0.439750	−	0.517714i	−0.0545443	−	0.0642145i
$66$		0			0
$67$	5.53784	+	8.16770i	0.676554	+	0.997843i	0.998691	+	0.0511499i	$0.0162886\pi$
$67$	5.53784	+	8.16770i	0.676554	+	0.997843i	−0.322137	+	0.946693i	$0.604401\pi$
$68$	0.185553	+	0.349990i	0.0225016	+	0.0424425i
$69$		0			0
$70$	0.745590	−	2.68537i	0.0891150	−	0.320963i
$71$	−1.91968	−	4.81804i	−0.227824	−	0.571796i	0.769977	−	0.638072i	$-0.220268\pi$
$71$	−1.91968	−	4.81804i	−0.227824	−	0.571796i	−0.997801	+	0.0662758i	$0.978888\pi$
$72$		0			0
$73$	−10.7876	+	1.17323i	−1.26260	+	0.137316i	−0.714820	−	0.699309i	$-0.753491\pi$
$73$	−10.7876	+	1.17323i	−1.26260	+	0.137316i	−0.547777	+	0.836625i	$0.684526\pi$
$74$	−6.60313	+	5.01957i	−0.767598	+	0.583513i
$75$		0			0
$76$	2.19700	+	1.01644i	0.252013	+	0.116594i
$77$	1.59031	+	9.70048i	0.181233	+	1.10547i
$78$		0			0
$79$	6.91340	−	4.15966i	0.777819	−	0.467998i	−0.0704818	−	0.997513i	$-0.522454\pi$
$79$	6.91340	−	4.15966i	0.777819	−	0.467998i	0.848301	+	0.529515i	$0.177626\pi$
$80$	−0.00248603		0.000270372i	−0.000277946		3.02285e-5i
$81$		0			0
$82$	−0.0260535	+	0.158920i	−0.00287713	+	0.0175497i
$83$	−0.375926	−	6.93356i	−0.0412633	−	0.761057i	−0.943815	−	0.330475i	$-0.892791\pi$
$83$	−0.375926	−	6.93356i	−0.0412633	−	0.761057i	0.902552	−	0.430582i	$-0.141692\pi$
$84$		0			0
$85$	0.189975	−	0.179954i	0.0206057	−	0.0195188i
$86$	0.183098	−	3.37704i	0.0197439	−	0.364156i
$87$		0			0
$88$	−6.74606	+	2.27301i	−0.719132	+	0.242304i
$89$	4.70823	−	1.58639i	0.499071	−	0.168157i	−0.0584973	−	0.998288i	$-0.518631\pi$
$89$	4.70823	−	1.58639i	0.499071	−	0.168157i	0.557569	+	0.830131i	$0.311734\pi$
$90$		0			0
$91$	−0.175769	+	3.24187i	−0.0184256	+	0.339840i
$92$	−5.16880	+	4.89615i	−0.538885	+	0.510459i
$93$		0			0
$94$	−0.152904	−	2.82015i	−0.0157708	−	0.290876i
$95$	0.258701	−	1.57800i	0.0265421	−	0.161900i
$96$		0			0
$97$	−8.26507	−	0.898880i	−0.839191	−	0.0912675i	−0.321579	−	0.946883i	$-0.604213\pi$
$97$	−8.26507	−	0.898880i	−0.839191	−	0.0912675i	−0.517612	+	0.855615i	$0.673179\pi$
$98$	−6.17367	+	3.71458i	−0.623635	+	0.375229i
$99$		0			0
$100$	−0.866879	−	5.28773i	−0.0866879	−	0.528773i
$101$	9.20908	+	4.26057i	0.916338	+	0.423943i	0.820626	−	0.571466i	$-0.193625\pi$
$101$	9.20908	+	4.26057i	0.916338	+	0.423943i	0.0957121	+	0.995409i	$0.469487\pi$
$102$		0			0
$103$	3.84974	−	2.92650i	0.379326	−	0.288356i	−0.398086	−	0.917348i	$-0.630325\pi$
$103$	3.84974	−	2.92650i	0.379326	−	0.288356i	0.777412	+	0.628992i	$0.216532\pi$
$104$	−2.33737	+	0.254205i	−0.229198	+	0.0249268i
$105$		0			0
$106$	0.449921	+	1.12922i	0.0437002	+	0.109679i
$107$	−0.277417	+	0.999166i	−0.0268189	+	0.0965930i	−0.975748	−	0.218896i	$-0.929755\pi$
$107$	−0.277417	+	0.999166i	−0.0268189	+	0.0965930i	0.948929	+	0.315489i	$0.102168\pi$
$108$		0			0
$109$	3.98701	+	7.52031i	0.381887	+	0.720315i	0.997715	−	0.0675659i	$-0.0215233\pi$
$109$	3.98701	+	7.52031i	0.381887	+	0.720315i	−0.615828	+	0.787880i	$0.711178\pi$
$110$	1.00833	+	1.48717i	0.0961404	+	0.141796i
$111$		0			0
$112$	0.00773772	+	0.00910955i	0.000731146	+	0.000860771i
$113$	−2.88456	+	7.23969i	−0.271356	+	0.681053i	−0.999993	−	0.00384813i	$-0.998775\pi$
$113$	−2.88456	+	7.23969i	−0.271356	+	0.681053i	0.728636	+	0.684901i	$0.240154\pi$
$114$		0			0
$115$	4.02981	+	2.42466i	0.375782	+	0.226100i
$116$	−12.1869	−	4.10624i	−1.13152	−	0.381255i
$117$		0			0
$118$	6.70892	−	0.148445i	0.617606	−	0.0136654i
$119$	−1.25070			−0.114652
$120$		0			0
$121$	3.99511	+	2.40378i	0.363192	+	0.218525i
$122$	4.80890	+	3.65563i	0.435378	+	0.330965i
$123$		0			0
$124$	−7.42875	−	8.74581i	−0.667122	−	0.785397i
$125$	−6.91970	+	3.20139i	−0.618917	+	0.286341i
$126$		0			0
$127$	−6.02613	−	11.3665i	−0.534733	−	1.00861i	−0.992810	−	0.119701i	$-0.961806\pi$
$127$	−6.02613	−	11.3665i	−0.534733	−	1.00861i	0.458077	−	0.888913i	$-0.348538\pi$
$128$	−4.53373	+	5.33752i	−0.400729	+	0.471774i
$129$		0			0
$130$	0.219654	+	0.551290i	0.0192649	+	0.0483513i
$131$	−7.28471	+	13.7404i	−0.636468	+	1.20051i	0.330064	+	0.943959i	$0.392930\pi$
$131$	−7.28471	+	13.7404i	−0.636468	+	1.20051i	−0.966532	+	0.256547i	$0.917415\pi$
$132$		0			0
$133$	−6.08446	+	4.62528i	−0.527589	+	0.401063i
$134$	−2.30640	−	8.30691i	−0.199243	−	0.717608i
$135$		0			0
$136$	−0.146532	−	0.893806i	−0.0125650	−	0.0766432i
$137$	17.1960	−	3.78513i	1.46916	−	0.323386i	0.592917	−	0.805263i	$-0.297976\pi$
$137$	17.1960	−	3.78513i	1.46916	−	0.323386i	0.876238	+	0.481878i	$0.160045\pi$
$138$		0			0
$139$	−7.67056	−	0.834224i	−0.650609	−	0.0707580i	−0.223138	−	0.974787i	$-0.571630\pi$
$139$	−7.67056	−	0.834224i	−0.650609	−	0.0707580i	−0.427471	+	0.904029i	$0.640595\pi$
$140$	2.21405	−	3.26548i	0.187121	−	0.275984i
$141$		0			0
$142$	0.245306	+	4.52440i	0.0205856	+	0.379679i
$143$	−1.51961	−	1.43945i	−0.127076	−	0.120373i
$144$		0			0
$145$	−0.459911	+	8.48255i	−0.0381935	+	0.704438i
$146$	9.25844	+	2.03794i	0.766234	+	0.168661i
$147$		0			0
$148$	−11.1272	+	3.74918i	−0.914649	+	0.308181i
$149$	−8.38833	−	1.84641i	−0.687198	−	0.151264i	−0.142373	−	0.989813i	$-0.545473\pi$
$149$	−8.38833	−	1.84641i	−0.687198	−	0.151264i	−0.544826	+	0.838549i	$0.683404\pi$
$150$		0			0
$151$	−8.35127	+	7.91074i	−0.679616	+	0.643767i	−0.947527	−	0.319677i	$-0.896426\pi$
$151$	−8.35127	+	7.91074i	−0.679616	+	0.643767i	0.267910	+	0.963444i	$0.413667\pi$
$152$	−4.01828	−	3.80632i	−0.325926	−	0.308733i
$153$		0			0
$154$	1.38936	−	8.47473i	0.111958	−	0.682913i
$155$	−4.25384	+	6.27394i	−0.341676	+	0.503935i
$156$		0			0
$157$	−9.14935	+	5.50498i	−0.730197	+	0.439345i	−0.831510	−	0.555509i	$-0.812523\pi$
$157$	−9.14935	+	5.50498i	−0.730197	+	0.439345i	0.101313	+	0.994855i	$0.467696\pi$
$158$	−6.88402	+	1.51529i	−0.547663	+	0.120550i
$159$		0			0
$160$	4.19530	+	1.94095i	0.331668	+	0.153446i
$161$	−6.01363	−	21.6591i	−0.473941	−	1.70698i
$162$		0			0
$163$	−24.2738	+	2.63993i	−1.90127	+	0.206776i	−0.982269	−	0.187479i	$-0.939968\pi$
$163$	−24.2738	+	2.63993i	−1.90127	+	0.206776i	−0.919001	+	0.394254i	$0.871003\pi$
$164$	−0.106785	+	0.201418i	−0.00833852	+	0.0157281i
$165$		0			0
$166$	−1.62292	+	5.84521i	−0.125963	+	0.453677i
$167$	7.64744	−	9.00326i	0.591776	−	0.696693i	−0.382010	−	0.924158i	$-0.624768\pi$
$167$	7.64744	−	9.00326i	0.591776	−	0.696693i	0.973786	+	0.227465i	$0.0730438\pi$
$168$		0			0
$169$	6.90747	+	10.1878i	0.531344	+	0.783674i
$170$	−0.207481	+	0.0959910i	−0.0159131	+	0.00736218i
$171$		0			0
$172$	1.77210	−	4.44763i	0.135121	−	0.339129i
$173$	17.6657	+	13.4291i	1.34310	+	1.02100i	0.996553	+	0.0829625i	$0.0264382\pi$
$173$	17.6657	+	13.4291i	1.34310	+	1.02100i	0.346545	+	0.938033i	$0.387355\pi$
$174$		0			0
$175$	16.0320	+	5.40182i	1.21191	+	0.408340i
$176$	−0.00770573			−0.000580841
$177$		0			0
$178$	−4.34051			−0.325335
$179$	−15.6750	−	5.28151i	−1.17160	−	0.394759i	−0.334813	−	0.942284i	$-0.608673\pi$
$179$	−15.6750	−	5.28151i	−1.17160	−	0.394759i	−0.836789	+	0.547526i	$0.815570\pi$
$180$		0			0
$181$	−4.33412	−	3.29471i	−0.322153	−	0.244894i	0.431581	−	0.902074i	$-0.357956\pi$
$181$	−4.33412	−	3.29471i	−0.322153	−	0.244894i	−0.753733	+	0.657180i	$0.771749\pi$
$182$	1.04986	−	2.63494i	0.0778205	−	0.195315i
$183$		0			0
$184$	14.7740	−	6.83518i	1.08915	−	0.503896i
$185$	4.35275	+	6.41983i	0.320021	+	0.471995i
$186$		0			0
$187$	0.522014	−	0.614562i	0.0381734	−	0.0449412i
$188$	1.06962	−	3.85242i	0.0780100	−	0.280967i
$189$		0			0
$190$	−0.654372	+	1.23428i	−0.0474731	+	0.0895438i
$191$	−14.0776	+	1.53103i	−1.01862	+	0.110781i	−0.602162	−	0.798374i	$-0.705694\pi$
$191$	−14.0776	+	1.53103i	−1.01862	+	0.110781i	−0.416457	+	0.909156i	$0.636728\pi$
$192$		0			0
$193$	3.34590	+	12.0509i	0.240843	+	0.867439i	0.980838	+	0.194826i	$0.0624143\pi$
$193$	3.34590	+	12.0509i	0.240843	+	0.867439i	−0.739994	+	0.672613i	$0.765172\pi$
$194$	6.59197	+	3.04977i	0.473276	+	0.218961i
$195$		0			0
$196$	−9.96119	+	2.19262i	−0.711513	+	0.156616i
$197$	6.68590	−	4.02277i	0.476350	−	0.286611i	−0.257061	−	0.966395i	$-0.582754\pi$
$197$	6.68590	−	4.02277i	0.476350	−	0.286611i	0.733412	+	0.679784i	$0.237927\pi$
$198$		0			0
$199$	−7.38746	+	10.8957i	−0.523683	+	0.772375i	−0.993913	−	0.110169i	$-0.964861\pi$
$199$	−7.38746	+	10.8957i	−0.523683	+	0.772375i	0.470230	+	0.882544i	$0.344171\pi$
$200$	−1.98206	+	12.0901i	−0.140153	+	0.854896i
$201$		0			0
$202$	−6.43577	−	6.09628i	−0.452819	−	0.428933i
$203$	29.4774	−	27.9224i	2.06890	−	1.95977i
$204$		0			0
$205$	0.147073	+	0.0323732i	0.0102720	+	0.00226104i
$206$	−4.00359	+	1.34897i	−0.278943	+	0.0939870i
$207$		0			0
$208$	−0.00248554		0.000547109i	−0.000172341		3.79351e-5i
$209$	0.266767	−	4.92023i	0.0184526	−	0.340339i
$210$		0			0
$211$	−9.79699	−	9.28020i	−0.674452	−	0.638875i	0.271781	−	0.962359i	$-0.412387\pi$
$211$	−9.79699	−	9.28020i	−0.674452	−	0.638875i	−0.946234	+	0.323484i	$0.895146\pi$
$212$	0.0931605	+	1.71824i	0.00639829	+	0.118010i
$213$		0			0
$214$	0.508398	−	0.749831i	0.0347534	−	0.0512574i
$215$	−3.14406	−	0.341937i	−0.214423	−	0.0233199i
$216$		0			0
$217$	35.3826	−	7.78830i	2.40193	−	0.528704i
$218$	−1.20306	−	7.33832i	−0.0814812	−	0.497014i
$219$		0			0
$220$	0.680478	+	2.45086i	0.0458778	+	0.165237i
$221$	0.212013	−	0.161168i	0.0142616	−	0.0108414i
$222$		0			0
$223$	9.00369	−	16.9828i	0.602932	−	1.13725i	−0.374744	−	0.927129i	$-0.622269\pi$
$223$	9.00369	−	16.9828i	0.602932	−	1.13725i	0.977675	−	0.210121i	$-0.0673859\pi$
$224$	−8.17778	−	20.5247i	−0.546401	−	1.37136i
$225$		0			0
$226$	4.40769	−	5.18914i	0.293195	−	0.345176i
$227$	12.0843	+	22.7934i	0.802063	+	1.51285i	0.857556	+	0.514391i	$0.171982\pi$
$227$	12.0843	+	22.7934i	0.802063	+	1.51285i	−0.0554931	+	0.998459i	$0.517673\pi$
$228$		0			0
$229$	−0.546498	+	0.252837i	−0.0361136	+	0.0167079i	−0.437863	−	0.899042i	$-0.644264\pi$
$229$	−0.546498	+	0.252837i	−0.0361136	+	0.0167079i	0.401749	+	0.915750i	$0.368402\pi$
$230$	−2.65994	−	3.13153i	−0.175392	−	0.206487i
$231$		0			0
$232$	23.4081	+	17.7944i	1.53682	+	1.16826i
$233$	14.1686	+	8.52497i	0.928217	+	0.558490i	0.897488	−	0.441038i	$-0.145390\pi$
$233$	14.1686	+	8.52497i	0.928217	+	0.558490i	0.0307285	+	0.999528i	$0.490217\pi$
$234$		0			0
$235$	−2.64107			−0.172284
$236$	9.06729	+	2.83338i	0.590230	+	0.184437i
$237$		0			0
$238$	1.03547	+	0.348889i	0.0671193	+	0.0226151i
$239$	−6.03200	−	3.62934i	−0.390178	−	0.234762i	0.306924	−	0.951734i	$-0.400700\pi$
$239$	−6.03200	−	3.62934i	−0.390178	−	0.234762i	−0.697102	+	0.716972i	$0.745528\pi$
$240$		0			0
$241$	6.60563	−	16.5789i	0.425506	−	1.06794i	−0.547427	−	0.836853i	$-0.684393\pi$
$241$	6.60563	−	16.5789i	0.425506	−	1.06794i	0.972933	−	0.231086i	$-0.0742280\pi$
$242$	−2.63704	−	3.10456i	−0.169515	−	0.199569i
$243$		0			0
$244$	4.79888	+	7.07782i	0.307217	+	0.453111i
$245$	3.15595	+	5.95276i	0.201626	+	0.380308i
$246$		0			0
$247$	0.435384	−	1.56811i	0.0277029	−	0.0997766i
$248$	9.71127	+	24.3734i	0.616666	+	1.54771i
$249$		0			0
$250$	6.62192	−	0.720177i	0.418807	−	0.0455480i
$251$	−4.10594	+	3.12126i	−0.259165	+	0.197012i	−0.726686	−	0.686970i	$-0.758940\pi$
$251$	−4.10594	+	3.12126i	−0.259165	+	0.197012i	0.467521	+	0.883982i	$0.345147\pi$
$252$		0			0
$253$	13.1527	+	6.08508i	0.826902	+	0.382566i
$254$	1.81835	+	11.0914i	0.114093	+	0.695938i
$255$		0			0
$256$	13.7032	−	8.24495i	0.856451	−	0.515310i
$257$	4.25969	+	0.463270i	0.265712	+	0.0288980i	0.240005	−	0.970772i	$-0.422851\pi$
$257$	4.25969	+	0.463270i	0.265712	+	0.0288980i	0.0257070	+	0.999670i	$0.491816\pi$
$258$		0			0
$259$	5.99760	−	36.5837i	0.372672	−	2.27320i
$260$	0.0454815	+	0.838857i	0.00282064	+	0.0520237i
$261$		0			0
$262$	9.86403	−	9.34370i	0.609402	−	0.577256i
$263$	1.04514	−	19.2764i	0.0644460	−	1.18864i	−0.770183	−	0.637823i	$-0.779835\pi$
$263$	1.04514	−	19.2764i	0.0644460	−	1.18864i	0.834629	−	0.550813i	$-0.185682\pi$
$264$		0			0
$265$	1.07719	−	0.362948i	0.0661713	−	0.0222957i
$266$	6.32762	−	2.13202i	0.387971	−	0.130723i
$267$		0			0
$268$	0.660731	−	12.1865i	0.0403606	−	0.744407i
$269$	−18.8414	+	17.8476i	−1.14878	+	1.08818i	−0.153804	+	0.988101i	$0.549152\pi$
$269$	−18.8414	+	17.8476i	−1.14878	+	1.08818i	−0.994979	+	0.100083i	$0.968089\pi$
$270$		0			0
$271$	−0.904209	−	16.6772i	−0.0549268	−	1.01306i	−0.887983	−	0.459876i	$-0.847894\pi$
$271$	−0.904209	−	16.6772i	−0.0549268	−	1.01306i	0.833056	−	0.553188i	$-0.186589\pi$
$272$	0.000158616	0	0.000967512i	9.61748e−6	0	5.86640e-5i
$273$		0			0
$274$	−15.2926	−	1.66317i	−0.923860	−	0.100476i
$275$	−9.34571	+	5.62313i	−0.563567	+	0.339087i
$276$		0			0
$277$	4.49137	+	27.3961i	0.269860	+	1.64607i	0.679390	+	0.733778i	$0.262245\pi$
$277$	4.49137	+	27.3961i	0.269860	+	1.64607i	−0.409530	+	0.912297i	$0.634307\pi$
$278$	6.11781	+	2.83040i	0.366922	+	0.169756i
$279$		0			0
$280$	−7.18130	+	5.45909i	−0.429165	+	0.326243i
$281$	−26.0746	+	2.83578i	−1.55548	+	0.169168i	−0.845083	−	0.534635i	$-0.820449\pi$
$281$	−26.0746	+	2.83578i	−1.55548	+	0.169168i	−0.710395	+	0.703803i	$0.751484\pi$
$282$		0			0
$283$	−6.55463	−	16.4509i	−0.389633	−	0.977904i	−0.984705	−	0.174232i	$-0.944256\pi$
$283$	−6.55463	−	16.4509i	−0.389633	−	0.977904i	0.595072	−	0.803672i	$-0.297123\pi$
$284$	−1.71600	+	6.18048i	−0.101826	+	0.366744i
$285$		0			0
$286$	0.856554	+	1.61563i	0.0506491	+	0.0955344i
$287$	−0.403929	−	0.595751i	−0.0238432	−	0.0351661i
$288$		0			0
$289$	−10.9391	−	12.8786i	−0.643479	−	0.757562i
$290$	2.74701	−	6.89448i	0.161310	−	0.404858i
$291$		0			0
$292$	11.4993	+	6.91889i	0.672944	+	0.404897i
$293$	−23.6952	−	7.98384i	−1.38429	−	0.466421i	−0.474047	−	0.880499i	$-0.657207\pi$
$293$	−23.6952	−	7.98384i	−1.38429	−	0.466421i	−0.910241	+	0.414078i	$0.864104\pi$
$294$		0			0
$295$	0.201040	−	6.27200i	0.0117050	−	0.365170i
$296$	26.8470			1.56045
$297$		0			0
$298$	6.42970	+	3.86862i	0.372462	+	0.224103i
$299$	3.81045	+	2.89663i	0.220364	+	0.167516i
$300$		0			0
$301$	9.78585	+	11.5208i	0.564047	+	0.664047i
$302$	9.12082	−	4.21974i	0.524844	−	0.242819i
$303$		0			0
$304$	−0.00280637	−	0.00529337i	−0.000160956	−	0.000303595i
$305$	3.65693	−	4.30527i	0.209395	−	0.246519i
$306$		0			0
$307$	−1.55739	−	3.90875i	−0.0888849	−	0.223084i	0.877814	−	0.479003i	$-0.159002\pi$
$307$	−1.55739	−	3.90875i	−0.0888849	−	0.223084i	−0.966698	+	0.255918i	$0.917622\pi$
$308$	5.69455	−	10.7411i	0.324477	−	0.612029i
$309$		0			0
$310$	5.27193	−	4.00762i	0.299425	−	0.227617i
$311$	−8.56829	−	30.8602i	−0.485863	−	1.74992i	−0.646506	−	0.762909i	$-0.723771\pi$
$311$	−8.56829	−	30.8602i	−0.485863	−	1.74992i	0.160643	−	0.987013i	$-0.448643\pi$
$312$		0			0
$313$	−3.46161	−	21.1149i	−0.195662	−	1.19348i	−0.883786	−	0.467891i	$-0.845014\pi$
$313$	−3.46161	−	21.1149i	−0.195662	−	1.19348i	0.688125	−	0.725592i	$-0.258434\pi$
$314$	9.11046	−	2.00536i	0.514133	−	0.113169i
$315$		0			0
$316$	−9.92003	−	1.07887i	−0.558045	−	0.0606911i
$317$	14.8267	−	21.8677i	0.832749	−	1.22821i	−0.138551	−	0.990355i	$-0.544244\pi$
$317$	14.8267	−	21.8677i	0.832749	−	1.22821i	0.971300	−	0.237858i	$-0.0764453\pi$
$318$		0			0
$319$	1.41719	+	26.1386i	0.0793475	+	1.46348i
$320$	−2.92826	−	2.77379i	−0.163695	−	0.155060i
$321$		0			0
$322$	−1.06319	+	19.6093i	−0.0592490	+	1.09278i
$323$	0.612280	+	0.134773i	0.0340682	+	0.00749897i
$324$		0			0
$325$	−3.41377	+	1.15023i	−0.189362	+	0.0638034i
$326$	20.8329	+	4.58567i	1.15383	+	0.253977i
$327$		0			0
$328$	0.378425	−	0.358463i	0.0208950	−	0.0197928i
$329$	9.16441	+	8.68099i	0.505250	+	0.478599i
$330$		0			0
$331$	1.15543	−	7.04784i	0.0635084	−	0.387384i	−0.935877	−	0.352327i	$-0.885390\pi$
$331$	1.15543	−	7.04784i	0.0635084	−	0.387384i	0.999385	−	0.0350571i	$-0.0111613\pi$
$332$	−4.81930	+	7.10793i	−0.264493	+	0.390099i
$333$		0			0
$334$	−8.84288	+	5.32058i	−0.483861	+	0.291129i
$335$	−7.87339	+	1.73306i	−0.430169	+	0.0946874i
$336$		0			0
$337$	12.6940	+	5.87289i	0.691488	+	0.319916i	0.733971	−	0.679181i	$-0.237665\pi$
$337$	12.6940	+	5.87289i	0.691488	+	0.319916i	−0.0424830	+	0.999097i	$0.513527\pi$
$338$	−2.87683	−	10.3614i	−0.156479	−	0.563586i
$339$		0			0
$340$	−0.321731	+	0.0349903i	−0.0174483	+	0.00189762i
$341$	−10.9409	+	20.6367i	−0.592483	+	1.11754i
$342$		0			0
$343$	1.30279	−	4.69221i	0.0703439	−	0.253356i
$344$	−7.08674	+	8.34316i	−0.382092	+	0.449833i
$345$		0			0
$346$	−10.8795	−	16.0460i	−0.584883	−	0.862638i
$347$	−1.94940	+	0.901887i	−0.104649	+	0.0484158i	−0.471515	−	0.881858i	$-0.656293\pi$
$347$	−1.94940	+	0.901887i	−0.104649	+	0.0484158i	0.366866	+	0.930274i	$0.380431\pi$
$348$		0			0
$349$	−0.177200	+	0.444738i	−0.00948529	+	0.0238063i	−0.933643	−	0.358205i	$-0.883389\pi$
$349$	−0.177200	+	0.444738i	−0.00948529	+	0.0238063i	0.924158	+	0.382011i	$0.124768\pi$
$350$	−11.7662	−	8.94443i	−0.628930	−	0.478100i
$351$		0			0
$352$	13.4985	+	4.54817i	0.719472	+	0.242418i
$353$	5.34376			0.284419			0.142210	−	0.989837i	$-0.454579\pi$
$353$	5.34376			0.284419			0.142210	+	0.989837i	$0.454579\pi$
$354$		0			0
$355$	4.23710			0.224882
$356$	−5.82291	−	1.96197i	−0.308614	−	0.103984i
$357$		0			0
$358$	11.5041	+	8.74521i	0.608012	+	0.462199i
$359$	8.96480	−	22.5000i	0.473144	−	1.18750i	−0.477891	−	0.878419i	$-0.658599\pi$
$359$	8.96480	−	22.5000i	0.473144	−	1.18750i	0.951035	−	0.309083i	$-0.100022\pi$
$360$		0			0
$361$	−13.7669	+	6.36924i	−0.724573	+	0.335223i
$362$	2.66918	+	3.93674i	0.140289	+	0.206911i
$363$		0			0
$364$	2.59944	−	3.06029i	0.136248	−	0.160403i
$365$	2.37166	−	8.54195i	0.124138	−	0.447106i
$366$		0			0
$367$	1.66643	−	3.14323i	0.0869871	−	0.164075i	−0.836202	−	0.548422i	$-0.815229\pi$
$367$	1.66643	−	3.14323i	0.0869871	−	0.164075i	0.923189	+	0.384347i	$0.125573\pi$
$368$	0.0175176	−	0.00190516i	0.000913170	−	9.93132e-5i
$369$		0			0
$370$	−1.81284	−	6.52925i	−0.0942449	−	0.339440i
$371$	−4.93079	−	2.28123i	−0.255994	−	0.118435i
$372$		0			0
$373$	−28.8303	+	6.34602i	−1.49277	+	0.328584i	−0.885025	−	0.465544i	$-0.845859\pi$
$373$	−28.8303	+	6.34602i	−1.49277	+	0.328584i	−0.607750	+	0.794129i	$0.707928\pi$
$374$	−0.603614	+	0.363183i	−0.0312122	+	0.0187797i
$375$		0			0
$376$	−5.13011	+	7.56634i	−0.264565	+	0.390204i
$377$	−1.39872	+	8.53180i	−0.0720376	+	0.439410i
$378$		0			0
$379$	9.76424	+	9.24917i	0.501555	+	0.475098i	0.896146	−	0.443759i	$-0.146355\pi$
$379$	9.76424	+	9.24917i	0.501555	+	0.475098i	−0.394591	+	0.918857i	$0.629114\pi$
$380$	−1.43577	+	1.36003i	−0.0736533	+	0.0697681i
$381$		0			0
$382$	12.0820	+	2.65946i	0.618171	+	0.136070i
$383$	−7.74693	+	2.61025i	−0.395850	+	0.133377i	−0.510185	−	0.860065i	$-0.670423\pi$
$383$	−7.74693	+	2.61025i	−0.395850	+	0.133377i	0.114335	+	0.993442i	$0.463526\pi$
$384$		0			0
$385$	−7.84299	−	1.72637i	−0.399716	−	0.0879841i
$386$	0.591542	−	10.9104i	0.0301087	−	0.555322i
$387$		0			0
$388$	7.46477	+	7.07101i	0.378966	+	0.358976i
$389$	1.99545	+	36.8040i	0.101174	+	1.86604i	0.406321	+	0.913731i	$0.366812\pi$
$389$	1.99545	+	36.8040i	0.101174	+	1.86604i	−0.305147	+	0.952305i	$0.598706\pi$
$390$		0			0
$391$	−1.03476	+	1.52616i	−0.0523302	+	0.0771813i
$392$	23.1842	+	2.52143i	1.17098	+	0.127351i
$393$		0			0
$394$	−6.65748	+	1.46542i	−0.335399	+	0.0738269i
$395$	1.06639	+	6.50471i	0.0536560	+	0.327287i
$396$		0			0
$397$	8.38713	+	30.2077i	0.420938	+	1.51608i	0.805282	+	0.592892i	$0.202014\pi$
$397$	8.38713	+	30.2077i	0.420938	+	1.51608i	−0.384343	+	0.923190i	$0.625572\pi$
$398$	9.15554	−	6.95986i	0.458926	−	0.348866i
$399$		0			0
$400$	−0.00621192	+	0.0117169i	−0.000310596	+	0.000585846i
$401$	−4.21923	−	10.5895i	−0.210698	−	0.528813i	0.785205	−	0.619236i	$-0.212558\pi$
$401$	−4.21923	−	10.5895i	−0.210698	−	0.528813i	−0.995903	+	0.0904226i	$0.971178\pi$
$402$		0			0
$403$	−4.99427	+	5.87971i	−0.248783	+	0.292889i
$404$	−5.87816	−	11.0874i	−0.292449	−	0.551618i
$405$		0			0
$406$	−32.1936	+	14.8944i	−1.59774	+	0.739195i
$407$	15.4730	+	18.2162i	0.766969	+	0.902946i
$408$		0			0
$409$	−1.78829	−	1.35942i	−0.0884251	−	0.0672190i	0.560028	−	0.828474i	$-0.310790\pi$
$409$	−1.78829	−	1.35942i	−0.0884251	−	0.0672190i	−0.648453	+	0.761255i	$0.724584\pi$
$410$	−0.112732	−	0.0678287i	−0.00556745	−	0.00334982i
$411$		0			0
$412$	−5.98068			−0.294647
$413$	−21.3132	+	21.1028i	−1.04875	+	1.03840i
$414$		0			0
$415$	5.37584	+	1.81133i	0.263889	+	0.0889147i
$416$	4.03111	+	2.42544i	0.197642	+	0.118917i
$417$		0			0
$418$	−1.59338	+	3.99908i	−0.0779347	+	0.195601i
$419$	−6.93862	−	8.16878i	−0.338974	−	0.399071i	0.566092	−	0.824342i	$-0.308455\pi$
$419$	−6.93862	−	8.16878i	−0.338974	−	0.399071i	−0.905066	+	0.425271i	$0.860179\pi$
$420$		0			0
$421$	−0.227979	−	0.336244i	−0.0111110	−	0.0163875i	0.822093	−	0.569353i	$-0.192806\pi$
$421$	−0.227979	−	0.336244i	−0.0111110	−	0.0163875i	−0.833204	+	0.552966i	$0.813496\pi$
$422$	5.52225	+	10.4161i	0.268819	+	0.507046i
$423$		0			0
$424$	1.05257	−	3.79102i	0.0511174	−	0.184108i
$425$	−0.513652	−	1.28917i	−0.0249158	−	0.0625340i
$426$		0			0
$427$	−26.8405	+	2.91908i	−1.29890	+	0.141264i
$428$	1.02096	−	0.776116i	0.0493501	−	0.0375150i
$429$		0			0
$430$	2.50761	+	1.16014i	0.120928	+	0.0559471i
$431$	0.844787	+	5.15297i	0.0406919	+	0.248210i	0.999338	−	0.0363926i	$-0.0115867\pi$
$431$	0.844787	+	5.15297i	0.0406919	+	0.248210i	−0.958646	+	0.284602i	$0.908138\pi$
$432$		0			0
$433$	−8.60947	+	5.18014i	−0.413745	+	0.248942i	−0.707175	−	0.707039i	$-0.750031\pi$
$433$	−8.60947	+	5.18014i	−0.413745	+	0.248942i	0.293430	+	0.955980i	$0.405203\pi$
$434$	−31.4661	−	3.42215i	−1.51042	−	0.164268i
$435$		0			0
$436$	1.70308	−	10.3883i	0.0815629	−	0.497512i
$437$	0.610024	+	11.2512i	0.0291814	+	0.538219i
$438$		0			0
$439$	−16.4415	+	15.5742i	−0.784711	+	0.743318i	−0.970975	−	0.239182i	$-0.923121\pi$
$439$	−16.4415	+	15.5742i	−0.784711	+	0.743318i	0.186264	+	0.982500i	$0.440362\pi$
$440$	0.314857	−	5.80720i	0.0150102	−	0.276847i
$441$		0			0
$442$	−0.220486	+	0.0742904i	−0.0104875	+	0.00353364i
$443$	−7.03634	+	2.37082i	−0.334307	+	0.112641i	−0.481449	−	0.876474i	$-0.659889\pi$
$443$	−7.03634	+	2.37082i	−0.334307	+	0.112641i	0.147142	+	0.989115i	$0.452993\pi$
$444$		0			0
$445$	−0.219746	+	4.05298i	−0.0104170	+	0.192130i
$446$	−12.1917	+	11.5485i	−0.577291	+	0.546840i
$447$		0			0
$448$	1.04370	+	19.2499i	0.0493102	+	0.909473i
$449$	−4.99773	+	30.4848i	−0.235857	+	1.43867i	0.557635	+	0.830086i	$0.311709\pi$
$449$	−4.99773	+	30.4848i	−0.235857	+	1.43867i	−0.793492	+	0.608580i	$0.791739\pi$
$450$		0			0
$451$	0.461327	+	0.0501723i	0.0217230	+	0.00236252i
$452$	8.25859	−	4.96903i	0.388452	−	0.233724i
$453$		0			0
$454$	−3.64636	−	22.2418i	−0.171132	−	1.04386i
$455$	−2.40724	−	1.11371i	−0.112853	−	0.0522114i
$456$		0			0
$457$	8.40449	−	6.38893i	0.393145	−	0.298861i	−0.389863	−	0.920873i	$-0.627477\pi$
$457$	8.40449	−	6.38893i	0.393145	−	0.298861i	0.783008	+	0.622012i	$0.213684\pi$
$458$	0.522980	−	0.0568775i	0.0244372	−	0.00265771i
$459$		0			0
$460$	−2.15290	−	5.40336i	−0.100379	−	0.251933i
$461$	10.5183	−	37.8834i	0.489885	−	1.76441i	−0.142546	−	0.989788i	$-0.545529\pi$
$461$	10.5183	−	37.8834i	0.489885	−	1.76441i	0.632431	−	0.774617i	$-0.282057\pi$
$462$		0			0
$463$	−15.3690	−	28.9891i	−0.714259	−	1.34724i	−0.928822	−	0.370526i	$-0.879178\pi$
$463$	−15.3690	−	28.9891i	−0.714259	−	1.34724i	0.214563	−	0.976710i	$-0.431167\pi$
$464$	0.0178617	+	0.0263441i	0.000829211	+	0.00122299i
$465$		0			0
$466$	−9.35223	−	11.0103i	−0.433234	−	0.510042i
$467$	6.28278	−	15.7686i	0.290732	−	0.729683i	−0.708969	−	0.705240i	$-0.750839\pi$
$467$	6.28278	−	15.7686i	0.290732	−	0.729683i	0.999701	−	0.0244431i	$-0.00778127\pi$
$468$		0			0
$469$	33.0168	+	19.8655i	1.52457	+	0.917306i
$470$	2.18656	+	0.736739i	0.100859	+	0.0339832i
$471$		0			0
$472$	−17.5780	−	12.7589i	−0.809094	−	0.587277i
$473$	−9.74539			−0.448094
$474$		0			0
$475$	−7.26638	−	4.37203i	−0.333404	−	0.200603i
$476$	1.23140	+	0.936089i	0.0564413	+	0.0429056i
$477$		0			0
$478$	3.98153	+	4.68741i	0.182111	+	0.214397i
$479$	−34.7991	+	16.0998i	−1.59001	+	0.735618i	−0.997549	−	0.0699783i	$-0.977707\pi$
$479$	−34.7991	+	16.0998i	−1.59001	+	0.735618i	−0.592464	+	0.805597i	$0.701845\pi$
$480$		0			0
$481$	3.69757	+	6.97436i	0.168595	+	0.318004i
$482$	−10.0936	+	11.8831i	−0.459752	+	0.541261i
$483$		0			0
$484$	−2.13436	−	5.35683i	−0.0970162	−	0.243492i
$485$	3.18147	−	6.00089i	0.144463	−	0.272486i
$486$		0			0
$487$	11.5937	−	8.81332i	0.525362	−	0.399370i	−0.308600	−	0.951192i	$-0.599860\pi$
$487$	11.5937	−	8.81332i	0.525362	−	0.399370i	0.833962	+	0.551822i	$0.186067\pi$
$488$	−5.23072	−	18.8393i	−0.236784	−	0.852817i
$489$		0			0
$490$	−0.952289	−	5.80871i	−0.0430200	−	0.262411i
$491$	18.1700	−	3.99951i	0.819998	−	0.180495i	0.214890	−	0.976638i	$-0.431061\pi$
$491$	18.1700	−	3.99951i	0.819998	−	0.180495i	0.605109	+	0.796143i	$0.293130\pi$
$492$		0			0
$493$	−3.31106	−	0.360100i	−0.149123	−	0.0162181i
$494$	−0.797891	+	1.17680i	−0.0358988	+	0.0529468i
$495$		0			0
$496$	0.00153757	+	0.0283588i	6.90389e−5	+	0.00127335i
$497$	−14.7026	−	13.9270i	−0.659500	−	0.624712i
$498$		0			0
$499$	1.34480	−	24.8034i	0.0602016	−	1.11035i	−0.799868	−	0.600176i	$-0.795097\pi$
$499$	1.34480	−	24.8034i	0.0602016	−	1.11035i	0.860069	−	0.510177i	$-0.170420\pi$
$500$	9.20901	+	2.02706i	0.411840	+	0.0906527i
$501$		0			0
$502$	4.27003	−	1.43874i	0.190581	−	0.0642142i
$503$	−6.43350	−	1.41612i	−0.286856	−	0.0631417i	0.0692116	−	0.997602i	$-0.477952\pi$
$503$	−6.43350	−	1.41612i	−0.286856	−	0.0631417i	−0.356067	+	0.934460i	$0.615883\pi$
$504$		0			0
$505$	−6.01826	+	5.70080i	−0.267809	+	0.253682i
$506$	−9.19175	−	8.70689i	−0.408623	−	0.387068i
$507$		0			0
$508$	−2.57411	+	15.7014i	−0.114208	+	0.696636i
$509$	14.6581	−	21.6191i	0.649708	−	0.958248i	−0.350060	−	0.936727i	$-0.613839\pi$
$509$	14.6581	−	21.6191i	0.649708	−	0.958248i	0.999768	−	0.0215208i	$-0.00685080\pi$
$510$		0			0
$511$	−36.3063	+	21.8448i	−1.60610	+	0.966355i
$512$	0.0338210	−	0.00744456i	0.00149469	−	0.000329006i
$513$		0			0
$514$	−3.39740	−	1.57181i	−0.149853	−	0.0693294i
$515$	1.05692	+	3.80667i	0.0465733	+	0.167742i
$516$		0			0
$517$	−8.09062	+	0.879908i	−0.355825	+	0.0386983i
$518$	−15.1707	+	28.6149i	−0.666561	+	1.25727i
$519$		0			0
$520$	0.513871	−	1.85080i	0.0225348	−	0.0811628i
$521$	−10.3749	+	12.2143i	−0.454533	+	0.535118i	−0.940921	−	0.338625i	$-0.890038\pi$
$521$	−10.3749	+	12.2143i	−0.454533	+	0.535118i	0.486388	+	0.873743i	$0.338314\pi$
$522$		0			0
$523$	−13.5986	−	20.0564i	−0.594624	−	0.877005i	0.404674	−	0.914461i	$-0.367385\pi$
$523$	−13.5986	−	20.0564i	−0.594624	−	0.877005i	−0.999298	+	0.0374559i	$0.988075\pi$
$524$	17.4563	−	8.07616i	0.762583	−	0.352809i
$525$		0			0
$526$	−6.24253	+	15.6676i	−0.272187	+	0.683139i
$527$	−2.36589	−	1.79850i	−0.103060	−	0.0783439i
$528$		0			0
$529$	−9.60875	−	3.23756i	−0.417772	−	0.140764i
$530$	−0.993061			−0.0431358
$531$		0			0
$532$	9.45237			0.409812
$533$	0.145242	+	0.0489377i	0.00629113	+	0.00211973i
$534$		0			0
$535$	−0.674420	−	0.512681i	−0.0291577	−	0.0221651i
$536$	−10.3285	+	25.9227i	−0.446125	+	1.11969i
$537$		0			0
$538$	20.5776	−	9.52023i	0.887165	−	0.410446i
$539$	11.6511	+	17.1842i	0.501850	+	0.740174i
$540$		0			0
$541$	27.7349	−	32.6520i	1.19241	−	1.40382i	0.299199	−	0.954191i	$-0.403281\pi$
$541$	27.7349	−	32.6520i	1.19241	−	1.40382i	0.893216	−	0.449628i	$-0.148444\pi$
$542$	−3.90357	+	14.0594i	−0.167673	+	0.603902i
$543$		0			0
$544$	−0.848911	+	1.60122i	−0.0363968	+	0.0686516i
$545$	−6.91310	+	0.751845i	−0.296125	+	0.0322055i
$546$		0			0
$547$	5.11264	+	18.4141i	0.218601	+	0.787329i	0.988764	+	0.149482i	$0.0477607\pi$
$547$	5.11264	+	18.4141i	0.218601	+	0.787329i	−0.770164	+	0.637846i	$0.779826\pi$
$548$	−19.7637	−	9.14365i	−0.844262	−	0.390597i
$549$		0			0
$550$	9.30599	−	2.04840i	0.396809	−	0.0873442i
$551$	−17.4395	+	10.4930i	−0.742946	+	0.447016i
$552$		0			0
$553$	17.6801	−	26.0762i	0.751835	−	1.10887i
$554$	3.92384	−	23.9344i	0.166708	−	1.01687i
$555$		0			0
$556$	6.92783	+	6.56239i	0.293805	+	0.278307i
$557$	24.5389	−	23.2445i	1.03975	−	0.984900i	0.0398487	−	0.999206i	$-0.487312\pi$
$557$	24.5389	−	23.2445i	1.03975	−	0.984900i	0.999898	+	0.0143057i	$0.00455379\pi$
$558$		0			0
$559$	−3.14345	−	0.691925i	−0.132954	−	0.0292653i
$560$	−0.00925342	+	0.00311784i	−0.000391028	+	0.000131753i
$561$		0			0
$562$	22.3784	+	4.92586i	0.943976	+	0.207785i
$563$	−1.86724	+	34.4393i	−0.0786949	+	1.45144i	0.646508	+	0.762907i	$0.276229\pi$
$563$	−1.86724	+	34.4393i	−0.0786949	+	1.45144i	−0.725203	+	0.688535i	$0.758254\pi$
$564$		0			0
$565$	−4.62224	−	4.37842i	−0.194459	−	0.184201i
$566$	0.837581	+	15.4483i	0.0352062	+	0.649339i
$567$		0			0
$568$	8.23029	−	12.1388i	0.345335	−	0.509331i
$569$	39.7854	+	4.32693i	1.66789	+	0.181394i	0.892800	−	0.450454i	$-0.148738\pi$
$569$	39.7854	+	4.32693i	1.66789	+	0.181394i	0.775093	+	0.631848i	$0.217703\pi$
$570$		0			0
$571$	0.432666	−	0.0952370i	0.0181065	−	0.00398554i	−0.205908	−	0.978571i	$-0.566015\pi$
$571$	0.432666	−	0.0952370i	0.0181065	−	0.00398554i	0.224014	+	0.974586i	$0.428084\pi$
$572$	0.418804	+	2.55459i	0.0175111	+	0.106813i
$573$		0			0
$574$	0.168229	+	0.605905i	0.00702173	+	0.0252900i
$575$	19.8556	−	15.0938i	0.828035	−	0.629456i
$576$		0			0
$577$	−9.43862	+	17.8031i	−0.392935	+	0.741154i	−0.998506	−	0.0546369i	$-0.982600\pi$
$577$	−9.43862	+	17.8031i	−0.392935	+	0.741154i	0.605571	+	0.795791i	$0.292945\pi$
$578$	5.46408	+	13.7138i	0.227276	+	0.570419i
$579$		0			0
$580$	6.80159	−	8.00745i	0.282420	−	0.332491i
$581$	−12.7002	−	23.9552i	−0.526895	−	0.993829i
$582$		0			0
$583$	3.17893	−	1.47073i	0.131658	−	0.0609114i
$584$	−19.8648	−	23.3867i	−0.822013	−	0.967748i
$585$		0			0
$586$	17.3903	+	13.2198i	0.718387	+	0.546104i
$587$	29.5989	+	17.8090i	1.22168	+	0.735058i	0.972388	−	0.233371i	$-0.0749757\pi$
$587$	29.5989	+	17.8090i	1.22168	+	0.735058i	0.249288	+	0.968429i	$0.419803\pi$
$588$		0			0
$589$	−18.1607			−0.748301
$590$	−1.91605	+	5.13656i	−0.0788824	+	0.211469i
$591$		0			0
$592$	0.0275396	+	0.00927918i	0.00113187	+	0.000381372i
$593$	−1.72416	−	1.03739i	−0.0708027	−	0.0426006i	0.479712	−	0.877426i	$-0.340741\pi$
$593$	−1.72416	−	1.03739i	−0.0708027	−	0.0426006i	−0.550515	+	0.834825i	$0.685569\pi$
$594$		0			0
$595$	0.378200	−	0.949210i	0.0155047	−	0.0389138i
$596$	6.87695	+	8.09617i	0.281691	+	0.331632i
$597$		0			0
$598$	−2.34667	−	3.46108i	−0.0959626	−	0.141534i
$599$	−22.5825	−	42.5951i	−0.922696	−	1.74039i	−0.614172	−	0.789173i	$-0.710510\pi$
$599$	−22.5825	−	42.5951i	−0.922696	−	1.74039i	−0.308524	−	0.951216i	$-0.599835\pi$
$600$		0			0
$601$	−1.84924	+	6.66037i	−0.0754322	+	0.271682i	−0.991643	−	0.129015i	$-0.958818\pi$
$601$	−1.84924	+	6.66037i	−0.0754322	+	0.271682i	0.916210	+	0.400697i	$0.131232\pi$
$602$	−4.88800	−	12.2680i	−0.199220	−	0.500005i
$603$		0			0
$604$	14.1432	−	1.53817i	0.575479	−	0.0625871i
$605$	−3.03241	+	2.30518i	−0.123285	+	0.0937188i
$606$		0			0
$607$	−13.3571	−	6.17963i	−0.542146	−	0.250824i	0.129650	−	0.991560i	$-0.458615\pi$
$607$	−13.3571	−	6.17963i	−0.542146	−	0.250824i	−0.671796	+	0.740736i	$0.734477\pi$
$608$	1.79173	+	10.9290i	0.0726641	+	0.443231i
$609$		0			0
$610$	−4.22857	+	2.54425i	−0.171210	+	0.103014i
$611$	−2.67216	−	0.290615i	−0.108104	−	0.0117570i
$612$		0			0
$613$	−0.690535	+	4.21208i	−0.0278904	+	0.170124i	−0.997099	−	0.0761178i	$-0.975747\pi$
$613$	−0.690535	+	4.21208i	−0.0278904	+	0.170124i	0.969208	+	0.246242i	$0.0791958\pi$
$614$	0.199010	+	3.67053i	0.00803140	+	0.148131i
$615$		0			0
$616$	−20.1803	+	19.1158i	−0.813089	+	0.770199i
$617$	0.212106	−	3.91206i	0.00853906	−	0.157494i	−0.991154	−	0.132717i	$-0.957630\pi$
$617$	0.212106	−	3.91206i	0.00853906	−	0.157494i	0.999693	−	0.0247766i	$-0.00788743\pi$
$618$		0			0
$619$	−40.4111	+	13.6161i	−1.62426	+	0.547276i	−0.976676	−	0.214719i	$-0.931116\pi$
$619$	−40.4111	+	13.6161i	−1.62426	+	0.547276i	−0.647582	+	0.761996i	$0.724220\pi$
$620$	8.88393	−	2.99334i	0.356787	−	0.120216i
$621$		0			0
$622$	−1.51484	+	27.9396i	−0.0607395	+	1.12027i
$623$	14.0843	−	13.3414i	0.564277	−	0.534511i
$624$		0			0
$625$	0.835580	+	15.4114i	0.0334232	+	0.616454i
$626$	−3.02420	+	18.4468i	−0.120871	+	0.737283i
$627$		0			0
$628$	13.1284	+	1.42780i	0.523879	+	0.0569753i
$629$	−2.60568	+	1.56779i	−0.103895	+	0.0625118i
$630$		0			0
$631$	3.16887	+	19.3293i	0.126151	+	0.769486i	0.971810	+	0.235763i	$0.0757590\pi$
$631$	3.16887	+	19.3293i	0.126151	+	0.769486i	−0.845660	+	0.533722i	$0.820793\pi$
$632$	20.7066	+	9.57989i	0.823664	+	0.381067i
$633$		0			0
$634$	−18.3752	+	13.9685i	−0.729774	+	0.554760i
$635$	10.4487	−	1.13637i	0.414646	−	0.0450954i
$636$		0			0
$637$	2.53808	+	6.37010i	0.100562	+	0.252393i
$638$	6.11817	−	22.0357i	0.242221	−	0.872400i
$639$		0			0
$640$	−2.67991	−	5.05484i	−0.105933	−	0.199810i
$641$	−15.6100	−	23.0230i	−0.616557	−	0.909354i	0.383341	−	0.923607i	$-0.374773\pi$
$641$	−15.6100	−	23.0230i	−0.616557	−	0.909354i	−0.999898	+	0.0142528i	$0.995463\pi$
$642$		0			0
$643$	8.07384	+	9.50526i	0.318401	+	0.374851i	0.897958	−	0.440081i	$-0.145050\pi$
$643$	8.07384	+	9.50526i	0.318401	+	0.374851i	−0.579557	+	0.814932i	$0.696774\pi$
$644$	−10.2900	+	25.8258i	−0.405481	+	1.01768i
$645$		0			0
$646$	−0.469316	−	0.282378i	−0.0184650	−	0.0111100i
$647$	40.3047	+	13.5802i	1.58454	+	0.533894i	0.967464	−	0.253008i	$-0.0814198\pi$
$647$	40.3047	+	13.5802i	1.58454	+	0.533894i	0.617078	+	0.786902i	$0.288316\pi$
$648$		0			0
$649$	−1.47374	−	19.2805i	−0.0578493	−	0.756828i
$650$	3.14715			0.123441
$651$		0			0
$652$	25.8751	+	15.5685i	1.01335	+	0.609711i
$653$	−7.83242	−	5.95405i	−0.306506	−	0.233000i	0.440602	−	0.897703i	$-0.354765\pi$
$653$	−7.83242	−	5.95405i	−0.306506	−	0.233000i	−0.747108	+	0.664703i	$0.768558\pi$
$654$		0			0
$655$	−8.22535	−	9.68363i	−0.321391	−	0.378371i
$656$	0.000512085	0	0.000236916i	1.99936e−5	0	9.25000e-6i
$657$		0			0
$658$	−5.16569	−	9.74352i	−0.201379	−	0.379842i
$659$	−17.5243	+	20.6312i	−0.682650	+	0.803677i	−0.988949	−	0.148258i	$-0.952633\pi$
$659$	−17.5243	+	20.6312i	−0.682650	+	0.803677i	0.306299	+	0.951935i	$0.400909\pi$
$660$		0			0
$661$	−0.661402	−	1.65999i	−0.0257255	−	0.0645663i	0.915553	−	0.402198i	$-0.131754\pi$
$661$	−0.661402	−	1.65999i	−0.0257255	−	0.0645663i	−0.941278	+	0.337631i	$0.890374\pi$
$662$	−2.92262	+	5.51265i	−0.113591	+	0.214255i
$663$		0			0
$664$	15.6315	−	11.8827i	0.606618	−	0.461139i
$665$	−1.67044	−	6.01638i	−0.0647769	−	0.233305i
$666$		0			0
$667$	−9.68420	−	59.0710i	−0.374974	−	2.28724i
$668$	−14.2679	+	3.14061i	−0.552043	+	0.121514i
$669$		0			0
$670$	7.00189	+	0.761501i	0.270507	+	0.0294194i
$671$	9.76822	−	14.4070i	0.377098	−	0.556178i
$672$		0			0
$673$	0.379066	+	6.99146i	0.0146119	+	0.269501i	0.996705	+	0.0811068i	$0.0258455\pi$
$673$	0.379066	+	6.99146i	0.0146119	+	0.269501i	−0.982093	+	0.188394i	$0.939672\pi$
$674$	−8.87123	−	8.40327i	−0.341707	−	0.323682i
$675$		0			0
$676$	0.824145	−	15.2005i	0.0316979	−	0.584633i
$677$	−39.8325	−	8.76781i	−1.53089	−	0.336974i	−0.631937	−	0.775020i	$-0.717740\pi$
$677$	−39.8325	−	8.76781i	−1.53089	−	0.336974i	−0.898953	+	0.438046i	$0.855671\pi$
$678$		0			0
$679$	−30.7640	+	10.3656i	−1.18061	+	0.397795i
$680$	0.722656	+	0.159069i	0.0277126	+	0.00610000i
$681$		0			0
$682$	14.8148	−	14.0333i	0.567287	−	0.537363i
$683$	8.38984	+	7.94728i	0.321028	+	0.304094i	0.831195	−	0.555982i	$-0.187657\pi$
$683$	8.38984	+	7.94728i	0.321028	+	0.304094i	−0.510166	+	0.860076i	$0.670416\pi$
$684$		0			0
$685$	−2.32721	+	14.1954i	−0.0889181	+	0.542377i
$686$	−2.38750	+	3.52130i	−0.0911553	+	0.134444i
$687$		0			0
$688$	−0.0101532	+	0.00610901i	−0.000387089	+	0.000232904i
$689$	1.12981	−	0.248690i	0.0430423	−	0.00947432i
$690$		0			0
$691$	−34.9491	−	16.1692i	−1.32953	−	0.615105i	−0.378899	−	0.925438i	$-0.623697\pi$
$691$	−34.9491	−	16.1692i	−1.32953	−	0.615105i	−0.950628	+	0.310333i	$0.899559\pi$
$692$	−7.34208	−	26.4438i	−0.279104	−	1.00524i
$693$		0			0
$694$	1.86551	−	0.202886i	0.0708137	−	0.00770145i
$695$	2.95263	−	5.56925i	0.112000	−	0.211254i
$696$		0			0
$697$	−0.0157955	+	0.0568903i	−0.000598297	+	0.00215487i
$698$	0.270767	−	0.318771i	0.0102487	−	0.0120657i
$699$		0			0
$700$	−11.7417	−	17.3177i	−0.443793	−	0.654546i
$701$	−19.1426	+	8.85631i	−0.723006	+	0.334498i	−0.746645	−	0.665222i	$-0.768337\pi$
$701$	−19.1426	+	8.85631i	−0.723006	+	0.334498i	0.0236393	+	0.999721i	$0.492475\pi$
$702$		0			0
$703$	−6.87830	+	17.2632i	−0.259420	+	0.651095i
$704$	−9.89451	−	7.52161i	−0.372913	−	0.283481i
$705$		0			0
$706$	−4.42414	−	1.49067i	−0.166505	−	0.0561020i
$707$	39.6212			1.49011
$708$		0			0
$709$	20.5292			0.770990			0.385495	−	0.922710i	$-0.374031\pi$
$709$	20.5292			0.770990			0.385495	+	0.922710i	$0.374031\pi$
$710$	−3.50793	−	1.18196i	−0.131650	−	0.0443581i
$711$		0			0
$712$	11.1844	+	8.50219i	0.419155	+	0.318633i
$713$	19.7700	−	49.6190i	0.740392	−	1.85824i
$714$		0			0
$715$	1.55197	−	0.718018i	0.0580404	−	0.0268524i
$716$	11.4802	+	16.9320i	0.429033	+	0.632777i
$717$		0			0
$718$	−13.6985	+	16.1271i	−0.511223	+	0.601859i
$719$	1.86707	−	6.72458i	0.0696300	−	0.250785i	−0.920541	−	0.390646i	$-0.872252\pi$
$719$	1.86707	−	6.72458i	0.0696300	−	0.250785i	0.990171	+	0.139861i	$0.0446656\pi$
$720$		0			0
$721$	8.84476	−	16.6830i	0.329396	−	0.621307i
$722$	13.1744	−	1.43281i	0.490302	−	0.0533236i
$723$		0			0
$724$	1.80131	+	6.48775i	0.0669453	+	0.241115i
$725$	40.8873	+	18.9165i	1.51852	+	0.702541i
$726$		0			0
$727$	45.7223	−	10.0642i	1.69575	−	0.373262i	0.741191	−	0.671294i	$-0.234261\pi$
$727$	45.7223	−	10.0642i	1.69575	−	0.373262i	0.954556	+	0.298032i	$0.0963303\pi$
$728$	−7.86654	+	4.73314i	−0.291553	+	0.175422i
$729$		0			0
$730$	−4.34633	+	6.41036i	−0.160865	+	0.237258i
$731$	0.200600	−	1.22361i	0.00741947	−	0.0452567i
$732$		0			0
$733$	37.9972	+	35.9928i	1.40346	+	1.32943i	0.878045	+	0.478578i	$0.158848\pi$
$733$	37.9972	+	35.9928i	1.40346	+	1.32943i	0.525413	+	0.850848i	$0.323911\pi$
$734$	−2.25647	+	2.13744i	−0.0832879	+	0.0788945i
$735$		0			0
$736$	−31.8109	−	7.00212i	−1.17257	−	0.258101i
$737$	−23.5418	+	7.93217i	−0.867175	+	0.292185i
$738$		0			0
$739$	−4.47779	−	0.985637i	−0.164718	−	0.0362572i	0.131846	−	0.991270i	$-0.457910\pi$
$739$	−4.47779	−	0.985637i	−0.164718	−	0.0362572i	−0.296564	+	0.955013i	$0.595841\pi$
$740$	0.519336	−	9.57859i	0.0190912	−	0.352116i
$741$		0			0
$742$	3.44588	+	3.26411i	0.126502	+	0.119829i
$743$	1.98385	+	36.5899i	0.0727803	+	1.34235i	0.775708	+	0.631092i	$0.217393\pi$
$743$	1.98385	+	36.5899i	0.0727803	+	1.34235i	−0.702928	+	0.711261i	$0.748124\pi$
$744$		0			0
$745$	3.93786	−	5.80791i	0.144272	−	0.212785i
$746$	25.6391	+	2.78842i	0.938713	+	0.102091i
$747$		0			0
$748$	−0.973928	+	0.214378i	−0.0356104	+	0.00783843i
$749$	0.655070	+	3.99575i	0.0239357	+	0.146002i
$750$		0			0
$751$	3.67919	+	13.2512i	0.134255	+	0.483544i	0.999852	−	0.0171975i	$-0.00547440\pi$
$751$	3.67919	+	13.2512i	0.134255	+	0.483544i	−0.865597	+	0.500742i	$0.833061\pi$
$752$	−0.00787764	+	0.00598843i	−0.000287268	+	0.000218375i
$753$		0			0
$754$	3.53800	−	6.67337i	0.128846	−	0.243030i
$755$	−3.47845	−	8.73025i	−0.126594	−	0.317726i
$756$		0			0
$757$	−9.51281	+	11.1993i	−0.345749	+	0.407047i	−0.907360	−	0.420354i	$-0.861906\pi$
$757$	−9.51281	+	11.1993i	−0.345749	+	0.407047i	0.561611	+	0.827401i	$0.310182\pi$
$758$	−5.50379	−	10.3812i	−0.199907	−	0.377064i
$759$		0			0
$760$	4.10386	−	1.89865i	0.148863	−	0.0688711i
$761$	−7.25071	−	8.53620i	−0.262838	−	0.309437i	0.614874	−	0.788625i	$-0.289207\pi$
$761$	−7.25071	−	8.53620i	−0.262838	−	0.309437i	−0.877712	+	0.479188i	$0.840931\pi$
$762$		0			0
$763$	26.4594	+	20.1139i	0.957896	+	0.728174i
$764$	15.0063	+	9.02897i	0.542908	+	0.326657i
$765$		0			0
$766$	7.14189			0.258047
$767$	0.893558	−	6.32371i	0.0322645	−	0.228336i
$768$		0			0
$769$	−34.4141	−	11.5955i	−1.24100	−	0.418143i	−0.379167	−	0.925328i	$-0.623789\pi$
$769$	−34.4141	−	11.5955i	−1.24100	−	0.418143i	−0.861837	+	0.507185i	$0.830686\pi$
$770$	6.01169	+	3.61712i	0.216646	+	0.130352i
$771$		0			0
$772$	5.72519	−	14.3692i	0.206054	−	0.517157i
$773$	24.0518	+	28.3160i	0.865084	+	1.01846i	0.999620	+	0.0275475i	$0.00876974\pi$
$773$	24.0518	+	28.3160i	0.865084	+	1.01846i	−0.134536	+	0.990909i	$0.542954\pi$
$774$		0			0
$775$	22.5592	+	33.2723i	0.810349	+	1.19518i
$776$	−11.0120	−	20.7709i	−0.395308	−	0.745630i
$777$		0			0
$778$	8.61459	−	31.0270i	0.308848	−	1.11237i
$779$	0.133546	+	0.335176i	0.00478479	+	0.0120089i
$780$		0			0
$781$	12.9799	−	1.41165i	0.464456	−	0.0505127i
$782$	1.28242	−	0.974869i	0.0458592	−	0.0348612i
$783$		0			0
$784$	0.0229108	+	0.0105997i	0.000818244	+	0.000378560i
$785$	−1.41129	−	8.60846i	−0.0503710	−	0.307249i
$786$		0			0
$787$	4.12927	−	2.48450i	0.147192	−	0.0885628i	−0.440052	−	0.897972i	$-0.645040\pi$
$787$	4.12927	−	2.48450i	0.147192	−	0.0885628i	0.587245	+	0.809409i	$0.300213\pi$
$788$	−9.59358	−	1.04336i	−0.341757	−	0.0371683i
$789$		0			0
$790$	0.931644	−	5.68277i	0.0331464	−	0.202184i
$791$	1.64747	+	30.3859i	0.0585774	+	1.08040i
$792$		0			0
$793$	4.17371	−	3.95355i	0.148213	−	0.140395i
$794$	1.48281	−	27.3489i	0.0526230	−	0.970575i
$795$		0			0
$796$	15.4284	−	5.19842i	0.546844	−	0.184253i
$797$	−1.08017	+	0.363952i	−0.0382617	+	0.0128919i	−0.338367	−	0.941014i	$-0.609875\pi$
$797$	−1.08017	+	0.363952i	−0.0382617	+	0.0128919i	0.300106	+	0.953906i	$0.402978\pi$
$798$		0			0
$799$	0.0560591	−	1.03395i	0.00198323	−	0.0365785i
$800$	17.7974	−	16.8586i	0.629234	−	0.596042i
$801$		0			0
$802$	0.539153	+	9.94409i	0.0190381	+	0.351138i
$803$	4.41945	−	26.9574i	0.155959	−	0.951307i
$804$		0			0
$805$	18.2565	+	1.98551i	0.643456	+	0.0699801i
$806$	5.77497	−	3.47469i	0.203415	−	0.122391i
$807$		0			0
$808$	4.64201	+	28.3150i	0.163305	+	0.996118i
$809$	18.0806	+	8.36499i	0.635681	+	0.294097i	0.711139	−	0.703052i	$-0.248180\pi$
$809$	18.0806	+	8.36499i	0.635681	+	0.294097i	−0.0754578	+	0.997149i	$0.524042\pi$
$810$		0			0
$811$	18.3506	−	13.9498i	0.644377	−	0.489843i	−0.231209	−	0.972904i	$-0.574268\pi$
$811$	18.3506	−	13.9498i	0.644377	−	0.489843i	0.875587	+	0.483061i	$0.160475\pi$
$812$	−49.9211	+	5.42925i	−1.75189	+	0.190529i
$813$		0			0
$814$	−7.72873	−	19.3976i	−0.270892	−	0.679887i
$815$	5.33659	−	19.2207i	0.186933	−	0.673271i
$816$		0			0
$817$	−3.54919	−	6.69449i	−0.124171	−	0.234211i
$818$	1.10132	+	1.62433i	0.0385068	+	0.0567932i
$819$		0			0
$820$	−0.120574	−	0.141951i	−0.00421062	−	0.00495713i
$821$	−5.81634	+	14.5979i	−0.202992	+	0.509471i	−0.994865	−	0.101215i	$-0.967727\pi$
$821$	−5.81634	+	14.5979i	−0.202992	+	0.509471i	0.791873	+	0.610686i	$0.209106\pi$
$822$		0			0
$823$	8.68095	+	5.22316i	0.302599	+	0.182068i	0.658753	−	0.752360i	$-0.271084\pi$
$823$	8.68095	+	5.22316i	0.302599	+	0.182068i	−0.356154	+	0.934427i	$0.615912\pi$
$824$	12.9586	+	4.36627i	0.451435	+	0.152106i
$825$		0			0
$826$	23.5321	−	11.5258i	0.818786	−	0.401033i
$827$	−26.3331			−0.915692			−0.457846	−	0.889032i	$-0.651379\pi$
$827$	−26.3331			−0.915692			−0.457846	+	0.889032i	$0.651379\pi$
$828$		0			0
$829$	−11.2551	−	6.77197i	−0.390906	−	0.235200i	0.306509	−	0.951868i	$-0.400839\pi$
$829$	−11.2551	−	6.77197i	−0.390906	−	0.235200i	−0.697415	+	0.716668i	$0.745667\pi$
$830$	−3.94542	−	2.99923i	−0.136948	−	0.104105i
$831$		0			0
$832$	−2.65751	−	3.12866i	−0.0921325	−	0.108467i
$833$	−2.39743	+	1.10917i	−0.0830659	+	0.0384304i
$834$		0			0
$835$	4.52044	+	8.52645i	0.156436	+	0.295070i
$836$	−3.94520	+	4.64464i	−0.136447	+	0.160638i
$837$		0			0
$838$	3.46582	+	8.69856i	0.119725	+	0.300487i
$839$	−18.4781	+	34.8533i	−0.637934	+	1.20327i	0.328048	+	0.944661i	$0.393609\pi$
$839$	−18.4781	+	34.8533i	−0.637934	+	1.20327i	−0.965982	+	0.258609i	$0.916736\pi$
$840$		0			0
$841$	62.9899	−	47.8837i	2.17207	−	1.65116i
$842$	0.0949488	+	0.341975i	0.00327215	+	0.0117852i
$843$		0			0
$844$	2.70005	+	16.4696i	0.0929395	+	0.566906i
$845$	−9.82066	+	2.16169i	−0.337841	+	0.0743644i
$846$		0			0
$847$	18.0993	+	1.96841i	0.621898	+	0.0676355i
$848$	0.00239003	−	0.00352503i	8.20739e−5	−	0.000121050i
$849$		0			0
$850$	0.0656369	+	1.21060i	0.00225133	+	0.0415233i
$851$	−39.6789	−	37.5859i	−1.36018	−	1.28843i
$852$		0			0
$853$	0.162864	−	3.00386i	0.00557637	−	0.102850i	−0.994420	−	0.105492i	$-0.966358\pi$
$853$	0.162864	−	3.00386i	0.00557637	−	0.102850i	0.999997	+	0.00264202i	$0.000840983\pi$
$854$	23.0357	+	5.07055i	0.788267	+	0.173511i
$855$		0			0
$856$	−2.77879	+	0.936282i	−0.0949770	+	0.0320015i
$857$	−3.98499	−	0.877162i	−0.136125	−	0.0299633i	0.146385	−	0.989228i	$-0.453236\pi$
$857$	−3.98499	−	0.877162i	−0.136125	−	0.0299633i	−0.282510	+	0.959264i	$0.591167\pi$
$858$		0			0
$859$	2.66233	−	2.52189i	0.0908375	−	0.0860459i	−0.640934	−	0.767596i	$-0.721453\pi$
$859$	2.66233	−	2.52189i	0.0908375	−	0.0860459i	0.731771	+	0.681550i	$0.238694\pi$
$860$	2.83962	+	2.68984i	0.0968304	+	0.0917226i
$861$		0			0
$862$	0.738040	−	4.50184i	0.0251377	−	0.153333i
$863$	−14.0391	+	20.7061i	−0.477897	+	0.704845i	−0.987859	−	0.155352i	$-0.950349\pi$
$863$	−14.0391	+	20.7061i	−0.477897	+	0.704845i	0.509963	+	0.860197i	$0.329659\pi$
$864$		0			0
$865$	−15.5338	+	9.34639i	−0.528166	+	0.317787i
$866$	8.57287	−	1.88703i	0.291318	−	0.0641240i
$867$		0			0
$868$	−40.6658	−	18.8140i	−1.38029	−	0.638589i
$869$	5.43390	+	19.5711i	0.184332	+	0.663906i
$870$		0			0
$871$	−8.15677	+	0.887102i	−0.276382	+	0.0300583i
$872$	−11.2743	+	21.2656i	−0.381796	+	0.720144i
$873$		0			0
$874$	2.63354	−	9.48515i	0.0890808	−	0.320840i
$875$	−19.2736	+	22.6906i	−0.651565	+	0.767082i
$876$		0			0
$877$	−12.5873	−	18.5649i	−0.425043	−	0.626892i	0.553521	−	0.832835i	$-0.313284\pi$
$877$	−12.5873	−	18.5649i	−0.425043	−	0.626892i	−0.978564	+	0.205944i	$0.933974\pi$
$878$	17.9566	−	8.30760i	0.606005	−	0.280368i
$879$		0			0
$880$	0.00233014	−	0.00584820i	7.85488e−5	−	0.000197143i
$881$	14.2220	+	10.8113i	0.479151	+	0.364241i	0.816696	−	0.577068i	$-0.195803\pi$
$881$	14.2220	+	10.8113i	0.479151	+	0.364241i	−0.337545	+	0.941309i	$0.609596\pi$
$882$		0			0
$883$	−0.715060	−	0.240932i	−0.0240637	−	0.00810800i	0.307244	−	0.951631i	$-0.400593\pi$
$883$	−0.715060	−	0.240932i	−0.0240637	−	0.00810800i	−0.331308	+	0.943523i	$0.607490\pi$
$884$	−0.329368			−0.0110779
$885$		0			0
$886$	6.48680			0.217928
$887$	−47.4862	−	16.0000i	−1.59443	−	0.537226i	−0.624587	−	0.780955i	$-0.714733\pi$
$887$	−47.4862	−	16.0000i	−1.59443	−	0.537226i	−0.969843	+	0.243729i	$0.921629\pi$
$888$		0			0
$889$	−39.9919	−	30.4010i	−1.34128	−	1.01962i
$890$	1.31253	−	3.29419i	0.0439960	−	0.110422i
$891$		0			0
$892$	−21.5755	+	9.98190i	−0.722402	+	0.334219i
$893$	−3.55098	−	5.23731i	−0.118829	−	0.175260i
$894$		0			0
$895$	8.74831	−	10.2993i	0.292424	−	0.344268i
$896$	−7.31570	+	26.3488i	−0.244400	+	0.880250i
$897$		0			0
$898$	12.6415	−	23.8445i	0.421854	−	0.795700i
$899$	95.9129	−	10.4312i	3.19887	−	0.347899i
$900$		0			0
$901$	0.119226	+	0.429412i	0.00397198	+	0.0143058i
$902$	−0.367940	−	0.170227i	−0.0122511	−	0.00566795i
$903$		0			0
$904$	−21.5220	+	4.73736i	−0.715812	+	0.157562i
$905$	3.81109	−	2.29305i	0.126685	−	0.0762237i
$906$		0			0
$907$	18.0877	−	26.6773i	0.600592	−	0.885807i	−0.398922	−	0.916985i	$-0.630616\pi$
$907$	18.0877	−	26.6773i	0.600592	−	0.885807i	0.999514	+	0.0311783i	$0.00992596\pi$
$908$	5.16190	−	31.4862i	0.171304	−	1.04491i
$909$		0			0
$910$	1.68230	+	1.59356i	0.0557677	+	0.0528259i
$911$	−5.54069	+	5.24842i	−0.183571	+	0.173888i	−0.773967	−	0.633226i	$-0.781730\pi$
$911$	−5.54069	+	5.24842i	−0.183571	+	0.173888i	0.590396	+	0.807114i	$0.298972\pi$
$912$		0			0
$913$	17.0717	+	3.75777i	0.564992	+	0.124364i
$914$	−8.74037	+	2.94497i	−0.289106	+	0.0974110i
$915$		0			0
$916$	0.727301	+	0.160091i	0.0240307	+	0.00528956i
$917$	−3.28769	+	60.6379i	−0.108569	+	2.00244i
$918$		0			0
$919$	−8.19068	−	7.75862i	−0.270185	−	0.255933i	0.540596	−	0.841282i	$-0.318199\pi$
$919$	−8.19068	−	7.75862i	−0.270185	−	0.255933i	−0.810781	+	0.585349i	$0.800957\pi$
$920$	0.719993	+	13.2795i	0.0237375	+	0.437812i
$921$		0			0
$922$	−19.2759	+	28.4298i	−0.634818	+	0.936287i
$923$	4.28698	+	0.466237i	0.141108	+	0.0153464i
$924$		0			0
$925$	40.1721	−	8.84254i	1.32085	−	0.290741i
$926$	4.63751	+	28.2875i	0.152398	+	0.929586i
$927$		0			0
$928$	−15.7401	−	56.6908i	−0.516695	−	1.86097i
$929$	3.89039	−	2.95739i	0.127639	−	0.0970290i	−0.539407	−	0.842045i	$-0.681351\pi$
$929$	3.89039	−	2.95739i	0.127639	−	0.0970290i	0.667046	+	0.745016i	$0.267558\pi$
$930$		0			0
$931$	−7.56121	+	14.2620i	−0.247809	+	0.467417i
$932$	−7.56947	−	18.9979i	−0.247946	−	0.622298i
$933$		0			0
$934$	−9.60028	+	11.3023i	−0.314131	+	0.369823i
$935$	0.308565	+	0.582015i	0.0100911	+	0.0190339i
$936$		0			0
$937$	8.99070	−	4.15954i	0.293713	−	0.135886i	−0.267499	−	0.963558i	$-0.586197\pi$
$937$	8.99070	−	4.15954i	0.293713	−	0.135886i	0.561212	+	0.827672i	$0.310335\pi$
$938$	−21.7933	−	25.6570i	−0.711576	−	0.837732i
$939$		0			0
$940$	2.60032	+	1.97671i	0.0848130	+	0.0644732i
$941$	−35.5662	−	21.3995i	−1.15942	−	0.697602i	−0.200063	−	0.979783i	$-0.564115\pi$
$941$	−35.5662	−	21.3995i	−1.15942	−	0.697602i	−0.959361	+	0.282181i	$0.908942\pi$
$942$		0			0
$943$	−1.06115			−0.0345558
$944$	−0.0136216	−	0.0191636i	−0.000443347	−	0.000623723i
$945$		0			0
$946$	8.06829	+	2.71852i	0.262323	+	0.0883868i
$947$	10.9215	+	6.57122i	0.354899	+	0.213536i	0.681827	−	0.731514i	$-0.261186\pi$
$947$	10.9215	+	6.57122i	0.354899	+	0.213536i	−0.326927	+	0.945049i	$0.606013\pi$
$948$		0			0
$949$	3.33951	−	8.38153i	0.108405	−	0.272076i
$950$	4.79629	+	5.64663i	0.155612	+	0.183201i
$951$		0			0
$952$	−1.98474	−	2.92727i	−0.0643258	−	0.0948735i
$953$	−0.589009	−	1.11099i	−0.0190799	−	0.0359885i	0.873789	−	0.486306i	$-0.161656\pi$
$953$	−0.589009	−	1.11099i	−0.0190799	−	0.0359885i	−0.892869	+	0.450317i	$0.851311\pi$
$954$		0			0
$955$	3.09496	−	11.1470i	0.100150	−	0.360709i
$956$	3.22255	+	8.08799i	0.104225	+	0.261584i
$957$		0			0
$958$	33.3016	−	3.62177i	1.07593	−	0.117014i
$959$	54.7344	−	41.6080i	1.76746	−	1.34359i
$960$		0			0
$961$	49.9960	+	23.1306i	1.61277	+	0.746148i
$962$	−1.11572	−	6.80559i	−0.0359722	−	0.219421i
$963$		0			0
$964$	−18.9122	+	11.3791i	−0.609120	+	0.366496i
$965$	−10.1577	−	1.10471i	−0.326986	−	0.0355619i
$966$		0			0
$967$	−1.72340	+	10.5123i	−0.0554208	+	0.338052i	0.944533	+	0.328417i	$0.106515\pi$
$967$	−1.72340	+	10.5123i	−0.0554208	+	0.338052i	−0.999954	+	0.00963490i	$0.996933\pi$
$968$	0.713793	+	13.1651i	0.0229422	+	0.423143i
$969$		0			0
$970$	−4.30794	+	4.08070i	−0.138320	+	0.131023i
$971$	−1.41244	+	26.0510i	−0.0453274	+	0.836015i	0.884165	+	0.467174i	$0.154728\pi$
$971$	−1.41244	+	26.0510i	−0.0453274	+	0.836015i	−0.929493	+	0.368841i	$0.879755\pi$
$972$		0			0
$973$	−28.5512	+	9.62001i	−0.915309	+	0.308403i
$974$	−12.0571	+	4.06250i	−0.386333	+	0.130171i
$975$		0			0
$976$	0.00114582	−	0.0211333i	3.66766e−5	−	0.000676461i
$977$	−12.9135	+	12.2323i	−0.413140	+	0.391347i	−0.865844	−	0.500314i	$-0.833218\pi$
$977$	−12.9135	+	12.2323i	−0.413140	+	0.391347i	0.452704	+	0.891661i	$0.350459\pi$
$978$		0			0
$979$	0.677136	+	12.4890i	0.0216414	+	0.399152i
$980$	1.34809	−	8.22298i	0.0430631	−	0.262674i
$981$		0			0
$982$	−16.1587	−	1.75737i	−0.515646	−	0.0560799i
$983$	−30.5131	+	18.3591i	−0.973216	+	0.585565i	−0.910960	−	0.412496i	$-0.864657\pi$
$983$	−30.5131	+	18.3591i	−0.973216	+	0.585565i	−0.0622564	+	0.998060i	$0.519830\pi$
$984$		0			0
$985$	1.03130	+	6.29065i	0.0328599	+	0.200437i
$986$	2.64080	+	1.22177i	0.0841003	+	0.0389090i
$987$		0			0
$988$	−1.60232	+	1.21805i	−0.0509766	+	0.0387514i
$989$	22.1544	−	2.40944i	0.704470	−	0.0766157i
$990$		0			0
$991$	10.6041	+	26.6144i	0.336852	+	0.845434i	0.995655	+	0.0931186i	$0.0296836\pi$
$991$	10.6041	+	26.6144i	0.336852	+	0.845434i	−0.658803	+	0.752315i	$0.728937\pi$
$992$	14.0448	−	50.5850i	0.445924	−	1.60607i
$993$		0			0
$994$	8.28737	+	15.6316i	0.262859	+	0.495805i
$995$	−6.03529	−	8.90139i	−0.191332	−	0.282193i
$996$		0			0
$997$	5.60285	+	6.59619i	0.177444	+	0.208903i	0.843693	−	0.536826i	$-0.180377\pi$
$997$	5.60285	+	6.59619i	0.177444	+	0.208903i	−0.666249	+	0.745730i	$0.732101\pi$
$998$	−8.03240	+	20.1598i	−0.254261	+	0.638147i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.64.2		140
3.2	odd	2		177.2.e.a.64.4	✓	140
59.12	even	29	inner	531.2.i.c.307.2		140
177.71	odd	58		177.2.e.a.130.4	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.64.4	✓	140	3.2	odd	2
177.2.e.a.130.4	yes	140	177.71	odd	58
531.2.i.c.64.2		140	1.1	even	1	trivial
531.2.i.c.307.2		140	59.12	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.827908 - 0.278955i) q^{2} +(-0.984570 - 0.748451i) q^{4} +(-0.302390 + 0.758941i) q^{5} +(3.54386 - 1.63956i) q^{7} +(1.58690 + 2.34050i) q^{8} +O(q^{10})\)	\(q+(-0.827908 - 0.278955i) q^{2} +(-0.984570 - 0.748451i) q^{4} +(-0.302390 + 0.758941i) q^{5} +(3.54386 - 1.63956i) q^{7} +(1.58690 + 2.34050i) q^{8} +(0.462061 - 0.543981i) q^{10} +(-0.673485 + 2.42568i) q^{11} +(-0.389461 + 0.734601i) q^{13} +(-3.39136 + 0.368832i) q^{14} +(0.000818890 + 0.00294937i) q^{16} +(-0.290699 - 0.134491i) q^{17} +(-1.91157 + 0.420768i) q^{19} +(0.865754 - 0.520907i) q^{20} +(1.23424 - 1.82036i) q^{22} +(0.931329 - 5.68086i) q^{23} +(3.14543 + 2.97951i) q^{25} +(0.527358 - 0.499540i) q^{26} +(-4.71631 - 1.03814i) q^{28} +(9.85394 - 3.32018i) q^{29} +(9.06141 + 1.99457i) q^{31} +(0.306328 - 5.64989i) q^{32} +(0.203155 + 0.192438i) q^{34} +(0.172706 + 3.18537i) q^{35} +(5.32796 - 7.85815i) q^{37} +(1.69998 + 0.184884i) q^{38} +(-2.25617 + 0.496620i) q^{40} +(-0.0298218 - 0.181905i) q^{41} +(1.03564 + 3.73006i) q^{43} +(2.47859 - 1.88418i) q^{44} +(-2.35576 + 4.44343i) q^{46} +(1.19658 + 3.00318i) q^{47} +(5.33907 - 6.28564i) q^{49} +(-1.77298 - 3.34419i) q^{50} +(0.933264 - 0.431774i) q^{52} +(-0.900748 - 1.06044i) q^{53} +(-1.63729 - 1.24464i) q^{55} +(9.46116 + 5.69259i) q^{56} -9.08434 q^{58} +(-7.22303 + 2.61302i) q^{59} +(-6.55238 - 2.20775i) q^{61} +(-6.94562 - 4.17904i) q^{62} +(-1.82741 + 4.58645i) q^{64} +(-0.439750 - 0.517714i) q^{65} +(5.53784 + 8.16770i) q^{67} +(0.185553 + 0.349990i) q^{68} +(0.745590 - 2.68537i) q^{70} +(-1.91968 - 4.81804i) q^{71} +(-10.7876 + 1.17323i) q^{73} +(-6.60313 + 5.01957i) q^{74} +(2.19700 + 1.01644i) q^{76} +(1.59031 + 9.70048i) q^{77} +(6.91340 - 4.15966i) q^{79} +(-0.00248603 - 0.000270372i) q^{80} +(-0.0260535 + 0.158920i) q^{82} +(-0.375926 - 6.93356i) q^{83} +(0.189975 - 0.179954i) q^{85} +(0.183098 - 3.37704i) q^{86} +(-6.74606 + 2.27301i) q^{88} +(4.70823 - 1.58639i) q^{89} +(-0.175769 + 3.24187i) q^{91} +(-5.16880 + 4.89615i) q^{92} +(-0.152904 - 2.82015i) q^{94} +(0.258701 - 1.57800i) q^{95} +(-8.26507 - 0.898880i) q^{97} +(-6.17367 + 3.71458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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